Given a pair of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair of normal extensions of and ; in other words, is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift is subnormal, then is subnormal if and only if a power is subnormal for some . As a corollary, we have that if is a 2-variable weighted shift having a tensor core or a diagonal core, then is subnormal if and only if a power of is subnormal.

中文翻译：

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多元加权移位的幂次正规性

给一对 通勤次正态希尔伯特空间算子的问题，通勤次正态提升问题（LPCS）要求通勤对存在的必要和充分条件 的正常延伸和; 换句话说，是次普通对。LPCS是运营商理论中一个长期存在的开放问题。在本文中，我们考虑了-可变加权移位的一类幂的LPCS 。我们的主要定理指出，如果2变量加权平移的“拐角”是次正规的，那么当且仅当有幂次时，才是次正规的 对某些人来说是不正常的 。作为推论，我们认为，如果是具有张量核心或对角核心的2变量加权移位，则当且仅当的幂次幂时，它才是次正规的。